Here is the full list of all 45 LEGO Marvel Super Heroes achievements. It takes around 30-35 hours to unlock all of the achievements on Windows.
Collect 1,000,000,000 studs (Single Player)
Destroy 100 vehicles in the Manhattan hub
Perform a special throwing move as Colossus on Wolverine
Collect all Avengers characters in the game (Single Player)
Collect Howard the Duck (Single Player)
Unlock Black Cat (Single Player)
Read a comic in Deadpool's room on the Helicarrier
Collect all Iron Man armors (Single Player)
Complete House Party Protocol
Complete Level 15 - The Good, the Bad and the Hungry
Complete Level 14 - A Doom with a View
Complete Level 13 - Magnetic Personality
Complete Level 12 - Rapturous Rise
Complete Level 11 - Taking Liberties
First time turning Mister Fantastic into a teapot
Complete Level 10 - That Sinking Feeling
Complete Level 9 - Doctor in the House
Defeat 100 enemies as the Thing
Create a custom character
Complete Level 8 - Juggernauts and Crosses
Complete Level 7 - Bifrosty Reception
Complete Level 6 - Red Head Detention
Play as Agent Coulson
Complete Level 5 - Rebooted, Resuited
Complete Level 4 - Rock up at the Lock up
Regenerate as Wolverine
Complete Level 3 - Exploratory Laboratory
Complete Level 2 - Times Square Off
Complete first Helicarrier skydive
Complete Level 1 - Sand Central Station
Team up Captain America with Human Torch (Co-op)
Rescue Stan Lee from every peril (Single Player)
Transform into the Hulk 50 times
Complete game 100% (Single Player)
Collect Doc Ock, Sandman, Mysterio, Kraven the Hunter, Electro and Vulture (Single Player)
Collect all traditionally heroic mutants (Single Player)
Collect all traditionally evil mutants (Single Player)
Turn into Stan Hulk
Create a character called “Trevor” in the character customizer
Perform Hulk's special move on Loki
Unlock all animal-themed characters (Single Player)
Unlock all the Guardians of the Galaxy (Single Player)
Drive to the Baxter Building as Magneto in the Magneto Mobile
Perform all big LEGO figure transformations
Unlock all True Believers (Single Player)